B0489
Title: BEAUTY powered BEAST
Authors: Kai Zhang - University of North Carolina at Chapel Hill (United States) [presenting]
Zhigen Zhao - Temple University (United States)
Wen Zhou - Colorado State University (United States)
Abstract: The focus is on nonparametric dependence detection with the proposed Binary Expansion Approximation of Uniformity (BEAUTY) approach, which generalizes the celebrated Euler's formula. It approximates the characteristic function of any copula with a linear combination of expectations of binary interactions from marginal binary expansions. This novel theory enables the unification of many important tests through approximations from some quadratic forms of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve robust power, we study test statistics with data-adaptive weights, referred to as the Binary Expansion Adaptive Symmetry Test (BEAST). By utilizing the properties of the binary expansion filtration, we show that the Neyman-Pearson test of uniformity can be approximated by an oracle-weighted sum of symmetry statistics. The BEAST with this oracle provides a benchmark of feasible power against any alternative by leading all existing tests with a substantial margin. To approach this oracle power, we develop the BEAST through a regularized resampling approximation of the oracle test. The BEAST improves the empirical power of many existing tests against a wide spectrum of common alternatives and provides a clear interpretation of the form of dependency when significant.
